Analysis and reanalysis of mechanical systems: concept of global near-regularity

Some near-regular mechanical systems involve global irregularities, wherein a large number of degrees of freedom are affected by irregularity. However, no efficient solution for such global near-regular systems has yet been developed. In this paper, methods for static and dynamic analyses/reanalyses of these systems are established using graph product rules combined with matrix analysis and linear algebra. Also, these methods are generalized to systems with nonlinear behavior. The developed formulations allow reduction in computational time and storage compared to those of conventional methods. As a practical example of a global near-regular mechanical system, a subject-specific finite element mechanical model of the human spine is developed and presented.